Here’s an interesting discovery to tack on some additional information - I still can’t see the cloak cross-faction on cloth or mail despite all the potential workarounds, but I somehow have the horde and alliance leather cloak appearance named “argent conscript’s cloak” despite never obtaining the leather cloak on any character. It doesn’t seem to share an appearance with anything else and is specifically named with an “argent” title. I think there is something mixed up on the backend with how the appearances are linked. I checked and do not have the plate cloak appearance (which I have not learned).
Additionally, the only way to gain the cross-faction appearance (in my case, the helm) from an item that I had already learned the appearance from a different item (which usually automatically gives a cross-faction equivalent but didn’t in these cases) was to buy that specific item (either faction, even if I “had the appearance” on the faction I bought it from) and put it in void storage.